On the Cartesian Product of Two Compact Spaces

On Set Coverings in Cartesian Product Spaces

Measures on the Product of Compact Spaces

If K is an uncountable metrizable compact space, we prove a “factorization” result for a wide variety of vector valued Borel measures μ defined onK. This result essentially says that for every such measure μ there exists a measure μ′ defined on K such that the measure μ of a product A1 × · · · × An of Borel sets of K equals the measure μ′ of the intersection A1 ∩ · · · ∩An, where the Ai’s are c...

Data dependence theorems for operators on cartesian product spaces

We present some abstract data dependence theorems of the fixed point set for operators f, g : X × Y → X × Y , using the c-Picard operators technique. 2000 Mathematical Subject Classification: 47H10.

On Extremal Set Partitions in Cartesian Product Spaces

Appendix: On Set Coverings in Cartesian Product Spaces

Consider (X, E), where X is a finite set and E is a system of subsets whose union equals X. For every natural number n ∈ N define the cartesian products Xn = ∏n 1 X and En = ∏n 1 E . The following problem is investigated: how many sets of En are needed to cover Xn? Let this number be denoted by c(n). It is proved that for all n ∈ N exp{C · n} ≤ c(n) ≤ exp{Cn+ log n+ log log |X|}+ 1. A formula f...